- 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...
-
Kurepa trees. The
existence of an
inaccessible cardinal is in fact
equiconsistent with the
failure of the
Kurepa hypothesis,
because if the
Kurepa hypothesis...
-
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...
-
theorists conjecture that
existence of a
strongly compact cardinal is
equiconsistent with that of a
supercompact cardinal. However, a
proof is
unlikely until...
- 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...
-
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...
- used this to show that
Euclidean geometry and
hyperbolic geometry were
equiconsistent so that
hyperbolic geometry was
logically consistent if and only if...
-
showed that NF is
equiconsistent with TST plus the
axiom scheme of "typical ambiguity".[citation needed] NF is also
equiconsistent with TST augmented...
