Definition of Equiconsistent. Meaning of Equiconsistent. Synonyms of Equiconsistent

- In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa. In...
- Beltrami who used these models to show that hyperbolic geometry was equiconsistent with Euclidean geometry. It is named after Henri Poincaré, because his...
- question is actually inconsistent. In case 1, we say that A1 and A2 are equiconsistent. In case 2, we say that A1 is consistency-wise stronger than A2 (vice...
- non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several weak systems of set theory. One such system is ZFC with...
- strength. If theories have the same proof-theoretic ordinal they are often equiconsistent, and if one theory has a larger proof-theoretic ordinal than another...
- theorists conjecture that existence of a strongly compact cardinal is equiconsistent with that of a supercompact cardinal. However, a proof is unlikely until...
- showed that NF is equiconsistent with TST plus the axiom scheme of "typical ambiguity".[citation needed] NF is also equiconsistent with TST augmented...
- choice (this is equivalent since these two theories have been proved equiconsistent; that is, if one is consistent, the same is true for the other). This...
- function s : N → N satisfies the Peano axioms. Peano arithmetic is equiconsistent with several weak systems of set theory. One such system is ZFC with...
- and the Kurepa hypothesis. The failure of the Kurepa hypothesis is equiconsistent with the existence of a strongly inaccessible cardinal. A variation...