On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice

Horst Herrlich, Paul Howard, and Eleftherios Tachtsis. "On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice." Bulletin of the Polish Academy of Sciences. Mathematics 63.2 (2015): 89-112. <http://eudml.org/doc/281232>.

@article{HorstHerrlich2015,
abstract = { We study the deductive strength of properties under basic set-theoretical operations of the subclass E-Fin of the Dedekind finite sets in set theory without the Axiom of Choice ( AC ), which consists of all E-finite sets, where a set X is called E-finite if for no proper subset Y of X is there a surjection f:Y → X. },
author = {Horst Herrlich, Paul Howard, Eleftherios Tachtsis},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {axiom of choice; notions of finite; finiteness classes; E-finite; E-fin finiteness class; ZFA- and ZF-models. the second- and third-named authors wish to dedicate this article to the memory of horst herrlich; who passed away on March 13; 2015},
language = {eng},
number = {2},
pages = {89-112},
title = {On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice},
url = {http://eudml.org/doc/281232},
volume = {63},
year = {2015},
}

TY - JOUR
AU - Horst Herrlich
AU - Paul Howard
AU - Eleftherios Tachtsis
TI - On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2015
VL - 63
IS - 2
SP - 89
EP - 112
AB - We study the deductive strength of properties under basic set-theoretical operations of the subclass E-Fin of the Dedekind finite sets in set theory without the Axiom of Choice ( AC ), which consists of all E-finite sets, where a set X is called E-finite if for no proper subset Y of X is there a surjection f:Y → X.
LA - eng
KW - axiom of choice; notions of finite; finiteness classes; E-finite; E-fin finiteness class; ZFA- and ZF-models. the second- and third-named authors wish to dedicate this article to the memory of horst herrlich; who passed away on March 13; 2015
UR - http://eudml.org/doc/281232
ER -