Saeed Salehi
Published 2022-09-15Version 1
Godelian sentences of a sufficiently strong and recursively enumerable theory, constructed in Godel's 1931 groundbreaking paper on the incompleteness theorems, are unprovable if the theory is consistent; however, they could be refutable. These sentences are independent when the theory is so-called omega-consistent; a notion introduced by Godel, which is stronger than (simple) consistency, but "much weaker" than soundness. Godel goes to great lengths to show in detail that omega-consistency is stronger than consistency, but never shows (or seems to forget to say) why it is much weaker than soundness. In this paper, we study this proof-theoretic notion and compare some of its properties with those of consistency and (variants of) soundness.
The Consistency of $ZFC+CIFS$
Consistency of partition relation for cardinal in (lambda,2^lambda)
A weak set theory that proves its own consistency
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