TY - JOUR
AU - Hsiung, Ming
AB - Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalize this result to the Liar-like paradox  for all ordinal   1. The main result is that for any positive integer n  2i(2j 1), the paradox n is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by 2i1; and for any ordinal   , the paradox  is paradoxical in a frame iff this frame contains at least an infinite walk that has an arbitrarily large depth. We thus get that n has a degree of paradoxicality no more than m iff the multiplicity of 2 in the (unique) prime factorization of n is no more than that in the prime factorization of m; and all tranfinite  has the same degree of paradoxcality but has a higher degree of paradoxicality than any n.
TI - Tarski's theorem and liar-like paradoxes
JF - Logic Journal of the IGPL
DO - 10.1093/jigpal/jzt020
DA - 2014-02-15
UR - https://www.deepdyve.com/lp/oxford-university-press/tarski-s-theorem-and-liar-like-paradoxes-xbfr0BgfWc
SP - 24
EP - 38
VL - 22
IS - 1
DP - DeepDyve
ER -