Generic families and models of set theory with the axiom of choice

Generic Families and Models of Set Theory with the Axiom of Choice

Let M be a countable transitive model of ZFC and i be a countable M -generic family of Cohen reals. We prove that there is no smallest transitive model A' of ZFC that either M u A ç N or A/U {A} ç N . h is also proved that there is no smallest transitive model N of ZFC~ (ZFC theory without the power set axiom) such that M U {A} ç N . It is also proved that certain classes of extensions of M obt...

the analysis of the role of the speech acts theory in translating and dubbing hollywood films

از محوری ترین اثراتی که یک فیلم سینمایی ایجاد می کند دیالوگ هایی است که هنرپیش گان فیلم میگویند. به زعم یک فیلم ساز, یک شیوه متأثر نمودن مخاطب از اثر منظوره نیروی گفتارهای گوینده, مثل نیروی عاطفی, ترس آور, غم انگیز, هیجان انگیز و غیره, است. این مطالعه به بررسی این مسأله مبادرت کرده است که آیا نیروی فراگفتاری هنرپیش گان به مثابه ی اعمال گفتاری در پنج فیلم هالیوودی در نسخه های دوبله شده باز تولید...

Axiom of Choice in nonstandard set theory

We verify that the best-known nonstandard set theories: IST, BST, and HST, with the Axiom of Choice deleted, are conservative extensions of ZF + Boolean Prime Ideal Theorem. 2010 Mathematics Subject Classification 26E35 (primary); 03E25, 03E70, 03H05 (secondary)

Mechanizing Set Theory: Cardinal Arithmetic and the Axiom of Choice

Fairly deep results of Zermelo-Frænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ⊗ κ = κ, where κ is any infinite cardinal. Proving this result required developing theories of orders, order-isomorphisms, order types, ordinal arithmetic, cardinals, e...

Mechanising Set Theory: Cardinal Arithmetic and the Axiom of Choice