Preserving Dependent Choice

• Autorzy: Karagila Asaf

Identyfikatory

DOI

10.4064/ba8169-12-2018

• Języki publikacji: EN

Abstrakty

EN

We prove some general theorems for preserving Dependent Choice when taking symmetric extensions, some of which are unwritten folklore results. We apply these to various constructions to obtain various simple consistency proofs.

Słowa kluczowe

EN

symmetric extensions; dependent choice; axiom of choice

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2019
• Tom: Vol. 67, no. 1
• Strony: 19--29
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Karagila Asaf

• School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

Bibliografia

• [1] A. W. Apter, On some questions concerning strong compactness, Arch. Math. Logic 51 (2012), 819-829.
• [2] D. Asperó and A. Karagila, Dependent choice, properness, and generic absoluteness, arXiv:1806.04077 (2018).
• [3] J. E. Baumgartner, Sacks forcing and the total failure of Martin’s axiom, Topology Appl. 19 (1985), 211-225.
• [4] M. Beriashvili, R. Schindler, L. Wu and L. Yu, Hamel bases and well-ordering the continuum, Proc. Amer. Math. Soc. 146 (2018), 3565-3573.
• [5] A. Blass, Injectivity, projectivity, and the axiom of choice, Trans. Amer. Math. Soc. 255 (1979), 31-59.
• [6] J. Brendle, F. Castiblanco, R. Schindler, L. Wu and L. Yu, A model with everything except for a well-ordering of the reals, arXiv:1809.10420 (2018).
• [7] Y. Hayut and A. Karagila, Spectra of uniformity, Comment. Math. Univ. Carolin., to appear.
• [8] W. Hodges, Six impossible rings, J. Algebra 31 (1974), 218-244.
• [9] W. Hodges, On the effectivity of some field constructions, Proc. London Math. Soc. (3) 32 (1976), 133-162.
• [10] T. J. Jech, The Axiom of Choice, Stud. Logic Found. Math. 75, North-Holland, Amsterdam, 1973.
• [11] A. Karagila, Vector spaces and antichains of cardinals in models of set theory, Master’s thesis, Ben-Gurion Univ. of the Negev, 2012.
• [12] A. Karagila, Embedding orders into the cardinals with DCκ, Fund. Math. 226 (2014), 143-156.
• [13] A. Karagila, Iterating symmetric extensions, J. Symbolic Logic 84 (2019), 123-159.
• [14] A. Karagila, The Morris model, arXiv:1811.10977 (2018).

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).