On Löwenheim-Skolem-Tarski numbers for extensions of first order logic
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| Publication date | 2011 |
| Journal | Journal of Mathematical Logic |
| Volume | Issue number | 11 | 1 |
| Pages (from-to) | 87-113 |
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| Abstract |
We show that, assuming the consistency of a supercompact cardinal, the first (weakly) inaccessible cardinal can satisfy a strong form of a Löwenheim-Skolem-Tarski theorem for the equicardinality logic L(I), a logic introduced in [5] strictly between first order logic and second order logic. On the other hand we show that in the light of present day inner model technology, nothing short of a supercompact cardinal suffices for this result. In particular, we show that the Löwenheim-Skolem-Tarski theorem for the equicardinality logic at κ implies the Singular Cardinals Hypothesis above κ as well as Projective Determinacy.
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| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1142/S0219061311001018 |
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