Combinatorial functions and indecomposable cardinals

Ellentuck, Erik

doi:10.1090/S0002-9939-1976-0409177-1

Combinatorial functions and indecomposable cardinals
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by Erik Ellentuck PDF

Proc. Amer. Math. Soc. 57 (1976), 311-317 Request permission

Abstract:

Combinatorial functions are used to replace indecomposable cardinals in certain types of set theoretic arguments. This allows us to extend decidability results from nonchoice set theories to set theories with a principle of linear ordering.

References

Robert Earl Bradford, Cardinal addition and the axiom of choice, Ann. Math. Logic 3 (1971), no. 2, 111–196. MR 300878, DOI 10.1016/0003-4843(71)90006-4

Undecidability of the theory of Dedekind cardinal addition

Erik Ellentuck, The structure of Dedekind cardinals, Trans. Amer. Math. Soc. 180 (1973), 109–125. MR 325396, DOI 10.1090/S0002-9947-1973-0325396-9
Erik Ellentuck and Alfred B. Manaster, The decidability of a class of $\textrm {AE}$ sentence in the isols, Pacific J. Math. 43 (1972), 573–584. MR 327499
Alfred B. Manaster, Higher-order indecomposable isols, Trans. Amer. Math. Soc. 125 (1966), 363–383. MR 224468, DOI 10.1090/S0002-9947-1966-0224468-3
John Myhill, Elementary properties of the group of isolic integers, Math. Z. 78 (1962), 126–130. MR 137651, DOI 10.1007/BF01195158
W. Szmielew, Elementary properties of Abelian groups, Fund. Math. 41 (1955), 203–271. MR 72131, DOI 10.4064/fm-41-2-203-271
Alfred Tarski, Cardinal Algebras. With an Appendix: Cardinal Products of Isomorphism Types, by Bjarni Jónsson and Alfred Tarski, Oxford University Press, New York, N. Y., 1949. MR 0029954