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There Is No Standard Model of ZFC and ZFC<sub>2</sub> with Henkin Semantics
Department of Mathematics, Israel Institute of Technology, Haifa, Israel
Lomonosov Moscow State University, Moscow, Russia
- 1 Department of Mathematics, Israel Institute of Technology, Haifa, Israel
- 2 Lomonosov Moscow State University, Moscow, Russia
Advances in Pure Mathematics·Volume 09 (2019)·Pages 685–744·Published 16 September 2019·DOI10.4236/apm.2019.99034
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Abstract
In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models or nonstandard model with standard part. A possible generalization of L ö b’s theorem is considered. Main results are: 1) , 2) , 3) , 4) , 5) let k be inaccessible cardinal then .
KeywordsGödel EncodingCompletion of <i>ZFC</i>Russell’s Paradox<i>ω</i>-ModelHenkin SemanticsFull Second-Order SemanticStrongly Inaccessible Cardinal
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