TY - GEN
T1 - Categoricity results for second-order ZF in dependent type theory
AU - Kirst, Dominik
AU - Smolka, Gert
N1 - Publisher Copyright:
© 2017, Springer International Publishing AG.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - We formalise the axiomatic set theory second-order ZF in the constructive type theory of Coq assuming excluded middle. In this setting we prove Zermelo’s embedding theorem for models, categoricity in all cardinalities, and the correspondence of inner models and Grothendieck universes. Our results are based on an inductive definition of the cumulative hierarchy eliminating the need for ordinals and transfinite recursion.
AB - We formalise the axiomatic set theory second-order ZF in the constructive type theory of Coq assuming excluded middle. In this setting we prove Zermelo’s embedding theorem for models, categoricity in all cardinalities, and the correspondence of inner models and Grothendieck universes. Our results are based on an inductive definition of the cumulative hierarchy eliminating the need for ordinals and transfinite recursion.
UR - http://www.scopus.com/inward/record.url?scp=85029521640&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-66107-0_20
DO - 10.1007/978-3-319-66107-0_20
M3 - Conference contribution
AN - SCOPUS:85029521640
SN - 9783319661063
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 304
EP - 318
BT - Interactive Theorem Proving - 8th International Conference, ITP 2017,Proceedings
A2 - Munoz, Cesar A.
A2 - Ayala-Rincon, Mauricio
PB - Springer Verlag
T2 - 8th International Conference on Interactive Theorem Proving, ITP 2017
Y2 - 26 September 2017 through 29 September 2017
ER -