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.
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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 |
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Inner Model of ZFC, Inaccessible Cardinal, Weakly Compact Cardinal, Lindelöf Space, Indestructible Space, N1 Borel Conjecture
| [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 |
APA Style
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
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
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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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}
}
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 -
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