Consistency Results in Topology and Homotopy Theory

Jaykov Foukzon

doi:doi:10.11648/j.pamj.s.2015040101.11

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Consistency Results in Topology and Homotopy Theory

Jaykov Foukzon

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 1-1)

Received: 10 October 2014 Accepted: 22 October 2014 Published: 31 October 2014

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Abstract

Main results is: (1) let κ be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = Hk )), (2) there is a Lindelöf T3 indestructible space of pseudocharacter ≤N1 and size N2 in L.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 1-1) This article belongs to the Special Issue Modern Combinatorial Set Theory and Large Cardinal Properties
DOI	10.11648/j.pamj.s.2015040101.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Inner Model of ZFC, Inaccessible Cardinal, Weakly Compact Cardinal, Lindelöf Space, Indestructible Space, N1 Borel Conjecture

References

[1]	M. H. Löb, Solution of a Problem of Leon Henkin. The Journal of Symbolic Logic 20 (2): 115-118.(1955)
[2]	C. Smorynski, Handbook of mathematical logic, Edited by J. Barwise. North-Holland Publishing Company, 1977
[3]	T. Drucker,Perspectives on the History of Mathematical Logic, Boston : Birkhauser, 2008.
[4]	A. Marcja, C. Toffalori, A guide to classical and modern model theory. Springer, 2003, 371 p. Series: Trends in Logic, Vol.19.
[5]	F. W. Lawvere, C. Maurer, G. C. Wraith, Model theory and topoi, ISBN: 978-3-540-07164-8
[6]	D. Marker, Model theory: an introduction.(Graduate Texts in Mathematics, Vol. 217). Springer 2002.
[7]	J. Foukzon, Generalized Löb's Theorem. http://arxiv.org/abs/1301.5340
[8]	J. Foukzon, An posible generalization of the Löb's theorem. AMS Sectional Meeting AMS Special Session.Spring Western Sectional Meeting University of Colorado Boulder, Boulder, CO April 13-14, 2013. Meeting #1089 http://www.ams.org/amsmtgs/2210_abstracts/1089-03-60.pdf
[9]	E. Mendelson, Introduction to Mathematical Logic, Edition: 4th,1997. ISBN-10: 0412808307
[10]	U. R. Schmerl, Iterated Reflection Principles and the ω-Rule.The Journal of Symbolic Logic, Vol. 47, No. 4, pp.721-733.
[11]	S. Feferman, Transfinite recursive progressions of axiomatic theories. Journal of Symbolic Logic 27:259-316.
[12]	S. Feferman,Systems of predicative analysis. Journal of Symbolic Logic 29:1-30.
[13]	S. Feferman, Reflecting on incompleteness. Journal of Symbolic Logic 56:1-49.
[14]	S. Feferman, C. Spector, Incompleteness along paths in progressions of theories. Journal of Symbolic Logic 27:383--390.
[15]	Kreisel, G. and A. Lévy, 1968. Reflection principles and their use for establishing the complexity of axiomatic systems. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 14:97-142.
[16]	P.Lindstrom, "First order predicate logic and generalized quantifiers", Theoria, Vol. 32, No.3. pp. 186-195, December 1966.
[17]	F.R. Drake," Set Theory: An Introduction to Large Cardinal", Studies in Logic and the Foundations of Mathematics,V.76. (1974). ISBN 0-444-105-35-2
[18]	A. Kanamori, "The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings (2003) Springer. ISBN 3-540-00384-3
[19]	W.V.O.,Quine, "New Foundation for Mathematical Logic," American Mathematical Monthly, vol. 44, (1937) pp. 70-80.
[20]	R.B.Jensen,"On the consistency of a slight (?) modification of Quine's 'New Foundation',"Synthese, vol.19 (1969),250-263.
[21]	M.R. Holmes,"The axiom of anti-foundation in Jensen's 'New Foundations with ur-elements,' " Bulletin de la Societe Mathematique de la Belgique, Series B.
[22]	M.R. Holmes, "Elementary Set Theory with a Universal Set," vol.10 of Cahiers du Centre de Logique, Universite Catholique de Louvain Lovain-la-Neuve, Belgium, 1998.
[23]	M.R. Holmes, "The Usual Model Construction for NFU Preserves Information," Notre Dame J. Formal Logic, Volume 53, Number 4 (2012), 571-580.
[24]	A. Enayat, "Automorphisms, Mahlo Cardinals,and NFU," AMS Special Session. Nonstandard models of Arithmetic and Set Theory. January 15-16 2003,Baltimore, Maryland.
[25]	R.M.Solovay, R.D. Arthan, J.Harrison, "The cosistency strengths of NFUB," Front for the arXiv,math/9707207
[26]	A. Brovykin, "On order-types of models of arithmetic". Ph.D. thesis pp.109, University of Birmingham 2000. http://logic.pdmi.ras.ru/~andrey/phd.pdf A.Brovykin,"Order-types of models of arithmetic and a connection with arithmetic saturation", Lobachevskii J. Math., 2004, Volume 16, Pages 3--15
[27]	P.J. Cohen, "Set Theory and the Continuum Hypothesis". ISBN: 9780486469218
[28]	F.D. Tall, On the cardinality of Lindelöf spaces with points G_δ , Topology and its Applications 63 (1995), 21--38.
[29]	R.R. Dias,F. D. Tall, Instituto de Matemática e Estatística Universidade de São Paulo,15-th Galway Topology Colloquium, Oxford, 2012.
[30]	J. Foukzon, Strong Reflection Principles and Large Cardinal Axioms. Fall Southeastern Sectional Meeting University of Louisville, Louisville, KY October 5-6, 2013 (Saturday - Sunday) Meeting #1092
[31]	J. Foukzon, Generalized Lob's Theorem. Strong Reflection Principles and Large Cardinal Axioms. Consistency Results in Topology,IX Iberoamerican Conference on Topology and its Applications 24-27 June, 2014 Almeria, Spain. Book of abstracts, p.66.
[32]	J. Foukzon, Generalized Löb's Theorem. Strong Reflection Principles and Large Cardinal Axioms. Consistency Results in Topology, International Conference on Topology and its Applications, July 3-7, 2014, Nafpaktos, Greece. Book of abstracts, p.81.
[33]	J. Foukzon, Generalized Lob's Theorem. Strong Reflection Principles and Large Cardinal Axioms. Consistency Results in Topology. http://arxiv.org/abs/1301.5340
[34]	F.D. Tall, Consistency results in topology, II: forcing and large cardinals (extended version), Topology Atlas: http://at.yorku.ca/p/a/a/o/08.htm
[35]	C.Casacubertaa, D.Scevenelsb, J. H. Smith, Implications of large-cardinal principles in homotopical localization, Advances in Mathematics 197 (2005) 120 – 139
[36]	D.G. Quillen, Homotopical Algebra, Lecture Notes in Mathematics, vol. 43, Springer, Berlin Heidelberg New York, 1967.
[37]	E. Dror Farjoun, Cellular Spaces, Null Spaces and Homotopy Localization, Lecture Notes in Math. vol. 1622, Springer-Verlag, Berlin Heidelberg New York, 1996.
[38]	C. Casacuberta, J. L. Rodr´ıguez, and D. Scevenels, Singly generated radicals associated with varieties of groups, in: Proceedings of Groups St Andrews 1997 in Bath, London Math. Soc. Lecture Note Ser. vol. 260, Cambridge University Press, Cambridge, 1999, 202–210.
[39]	T. Jech, Set Theory, Academic Press, New York, 1978.
[40]	D. Maharam. Problem 167. In D. Mauldin, editor, The Scottish Book, pages 240–243. Birkhauser, Boston, 1981.
[41]	Farah, Ilijas, and B. Veličković. "Von Neumann's Problem and Large Cardinals." Bulletin of the London Mathematical Society 38.6 (2006).
[42]	J. D. Hamkins and D. E. Seabold, Well-founded Boolean ultrapowers as large cardinal embeddings. http://arxiv.org/abs/1206.6075v1

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Jaykov Foukzon. (2014). Consistency Results in Topology and Homotopy Theory. Pure and Applied Mathematics Journal, 4(1-1), 1-5. https://doi.org/10.11648/j.pamj.s.2015040101.11

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ACS Style

Jaykov Foukzon. Consistency Results in Topology and Homotopy Theory. Pure Appl. Math. J. 2014, 4(1-1), 1-5. doi: 10.11648/j.pamj.s.2015040101.11

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AMA Style

Jaykov Foukzon. Consistency Results in Topology and Homotopy Theory. Pure Appl Math J. 2014;4(1-1):1-5. doi: 10.11648/j.pamj.s.2015040101.11

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@article{10.11648/j.pamj.s.2015040101.11,
  author = {Jaykov Foukzon},
  title = {Consistency Results in Topology and Homotopy Theory},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {1-1},
  pages = {1-5},
  doi = {10.11648/j.pamj.s.2015040101.11},
  url = {https://doi.org/10.11648/j.pamj.s.2015040101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040101.11},
  abstract = {Main results is: (1) let κ be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = Hk )), (2) there is a Lindelöf T3 indestructible space of pseudocharacter ≤N1 and size N2 in L.},
 year = {2014}
}

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TY  - JOUR
T1  - Consistency Results in Topology and Homotopy Theory
AU  - Jaykov Foukzon
Y1  - 2014/10/31
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.s.2015040101.11
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JF  - Pure and Applied Mathematics Journal
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AB  - Main results is: (1) let κ be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = Hk )), (2) there is a Lindelöf T3 indestructible space of pseudocharacter ≤N1 and size N2 in L.
VL  - 4
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Author Information

Jaykov Foukzon

Israel Institute of Technology, Department of Mathematics, Haifa, Israel

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Jaykov Foukzon. (2014). Consistency Results in Topology and Homotopy Theory. Pure and Applied Mathematics Journal, 4(1-1), 1-5. https://doi.org/10.11648/j.pamj.s.2015040101.11

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ACS Style

Jaykov Foukzon. Consistency Results in Topology and Homotopy Theory. Pure Appl. Math. J. 2014, 4(1-1), 1-5. doi: 10.11648/j.pamj.s.2015040101.11

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AMA Style

Jaykov Foukzon. Consistency Results in Topology and Homotopy Theory. Pure Appl Math J. 2014;4(1-1):1-5. doi: 10.11648/j.pamj.s.2015040101.11

Copy | Download

@article{10.11648/j.pamj.s.2015040101.11,
  author = {Jaykov Foukzon},
  title = {Consistency Results in Topology and Homotopy Theory},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {1-1},
  pages = {1-5},
  doi = {10.11648/j.pamj.s.2015040101.11},
  url = {https://doi.org/10.11648/j.pamj.s.2015040101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040101.11},
  abstract = {Main results is: (1) let κ be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = Hk )), (2) there is a Lindelöf T3 indestructible space of pseudocharacter ≤N1 and size N2 in L.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Consistency Results in Topology and Homotopy Theory
AU  - Jaykov Foukzon
Y1  - 2014/10/31
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.s.2015040101.11
DO  - 10.11648/j.pamj.s.2015040101.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.s.2015040101.11
AB  - Main results is: (1) let κ be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = Hk )), (2) there is a Lindelöf T3 indestructible space of pseudocharacter ≤N1 and size N2 in L.
VL  - 4
IS  - 1-1
ER  -

Copy | Download