Codings and strongly inaccessible cardinals. (English) Zbl 1417.03268
Summary: We show that a coding principle introduced by J. Moore with respect to all ladder systems is equiconsistent with the existence of a strongly inaccessible cardinal. We also show that a coding principle introduced by S. Todorcevic [Math. Res. Lett. 9, No. 4, 465–471 (2002; Zbl 1028.03040)] has consistency strength at least of a strongly inaccessible cardinal.
MSC:
| 03E50 | Continuum hypothesis and Martin’s axiom |
| 03E57 | Generic absoluteness and forcing axioms |
| 03E35 | Consistency and independence results |
| 03E55 | Large cardinals |
Keywords:
simplified morasses; strongly inaccessible cardinals; bounded Martin’s maximum; BPFA; \(\theta _{ac}\); \(v_{ac}\)Citations:
Zbl 1028.03040References:
| [1] | Devlin, K.J.: Constructibility, Perspectives in Mathematical Logic. Springer, Berlin (1984) · Zbl 0542.03029 |
| [2] | Miyamoto, T.: A coding and a strongly inaccessible cardinal (a note, 2008) · Zbl 1082.03042 |
| [3] | Moore, J.: Set mapping reflection. J. Math. Log. 5(1), 87-97 (2005) · Zbl 1082.03042 · doi:10.1142/S0219061305000407 |
| [4] | Todorcevic, S.: Generic absoluteness and the continuum. Math. Res. Lett. 9, 1-7 (2002) · Zbl 1028.03040 · doi:10.4310/MRL.2002.v9.n4.a6 |
| [5] | Velleman, D.: Simplified morasses. J. Symb. Log. 49(1), 257-271 (1984) · Zbl 0575.03035 · doi:10.2307/2274108 |
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