TY  - JOUR
AU  - WEBER, Z
Y2  - 2014/05/22
Y1  - 2010/03
SN  - 1755-0203
UR  - http://hdl.handle.net/11343/31746
AB  - <jats:p>This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis.</jats:p>
LA  - en
PB  - Cambridge University Press (CUP)
KW  - Philosophy
T1  - TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY
DO  - 10.1017/s1755020309990281
IS  - The Review of Symbolic Logic
VL  - 3
IS  - 1
SP  - 71-92
L1  - /bitstream/handle/11343/31746/281306_150541.pdf?sequence=1&isAllowed=n
ER  -