Results 1  10
of
30
MAHARAM ALGEBRAS AND COHEN REALS
, 2007
"... We show that the product of any two nonatomic Maharam algebras adds a Cohen real. As a corollary of this and a result of Shelah (1994) we obtain that the product of any two nonatomic ccc Souslin forcing notions adds a Cohen real. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We show that the product of any two nonatomic Maharam algebras adds a Cohen real. As a corollary of this and a result of Shelah (1994) we obtain that the product of any two nonatomic ccc Souslin forcing notions adds a Cohen real.
Between Maharam’s and von Neumann’s problems
, 2004
"... In the context of definable algebras Maharam’s and von Neumann’s problems essentially coincide. Consequently, random forcing is the only definable ccc forcing adding a single real that does not make the ground model reals null, and the only pairs of definable ccc σideals with the Fubini property ar ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
In the context of definable algebras Maharam’s and von Neumann’s problems essentially coincide. Consequently, random forcing is the only definable ccc forcing adding a single real that does not make the ground model reals null, and the only pairs of definable ccc σideals with the Fubini property
Subalgebras of Cohen algebras need not be
 Cohen, Proceedings of the A.S.L. Logic Colloquium
"... 504 revision:19970109 modified:19970109 Let us denote by Cκ the standard Cohen algebra of πweight κ, i.e. the complete Boolean algebra adjoining κ Cohen reals, where κ is an infinite cardinal or 0. More generally, we call a Boolean algebra A a Cohen algebra ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
504 revision:19970109 modified:19970109 Let us denote by Cκ the standard Cohen algebra of πweight κ, i.e. the complete Boolean algebra adjoining κ Cohen reals, where κ is an infinite cardinal or 0. More generally, we call a Boolean algebra A a Cohen algebra
CCC forcings and splitting reals
 Israel Journal of Mathematics
"... Abstract. Prikry asked if it is relatively consistent with the usual axioms of ZFC that every nontrivial ccc forcing adds either a Cohen or a random real. Both Cohen and random reals have the property that they neither contain nor are disjoint from an infinite set of integers in the ground model, i. ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
conjecture holds in the context of Souslin forcing notions, i.e. every non atomic ccc Souslin forcing either adds a Cohen real or its regular open algebra is a Maharam algebra. 1.
Complete embeddings of the Cohen algebra into three families of c.c.c., nonmeasurable Boolean algebras
 Pacific J. Math
, 2004
"... The Cohen algebra embeds as a complete subalgebra into three classic families of complete, atomless, c.c.c., nonmeasurable Boolean algebras; namely, the families of Argyros algebras andGalvinHajnal algebras, andthe atomless part of each Gaifman algebra. It immediately follows that the weak (ω, ω) ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The Cohen algebra embeds as a complete subalgebra into three classic families of complete, atomless, c.c.c., nonmeasurable Boolean algebras; namely, the families of Argyros algebras andGalvinHajnal algebras, andthe atomless part of each Gaifman algebra. It immediately follows that the weak (ω, ω
special are Cohen and random forcings i.e. Boolean algebras of the family of subsets of reals modulo meagre or null
 Israel Journal of Mathematics
, 1994
"... We prove that any Souslin c.c.c. forcing notion which add a non dominated real add a Cohen real. We also prove that any Souslin c.c.c. forcing add a real which is not on any old narrow tree. The feeling that those two forcing notionsCohen and Random (equivalently the (480) revision:20060615 modi ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
We prove that any Souslin c.c.c. forcing notion which add a non dominated real add a Cohen real. We also prove that any Souslin c.c.c. forcing add a real which is not on any old narrow tree. The feeling that those two forcing notionsCohen and Random (equivalently the (480) revision:2006
Handbook of Boolean Algebras
, 1989
"... Abstract. We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semiCohen algebras, pseudoCohen alg ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract. We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semiCohen algebras, pseudoCohen
COMPLETE CCC BOOLEAN ALGEBRAS, THE ORDER SEQUENTIAL TOPOLOGY, AND A PROBLEM Of Von Neumann
, 2005
"... Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B,τs) is topologically dense. 2. It is consistent that every weakly distributive complete cc ..."
Abstract

Cited by 24 (5 self)
 Add to MetaCart
ccc Boolean algebra carries a strictly positive Maharam submeasure. 3. The topological space (B,τs) is sequentially compact if and only if the generic extension by B does not add independent reals. Examples are also given of ccc forcings adding a real but not independent reals.
COMPLETE CCC BOOLEAN ALGEBRAS, THE ORDER SEQUENTIAL TOPOLOGY, AND A PROBLEM OF
, 2003
"... On the occasion of John von Neumann’s 100th birthday Abstract. Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B, τs) is topologically dense ..."
Abstract
 Add to MetaCart
dense. 2. It is consistent that every weakly distributive complete ccc Boolean algebra carries a strictly positive Maharam submeasure. 3. The topological space (B, τs) is sequentially compact if and only if the generic extension by B does not add independent reals. We also give examples of ccc forcings
ADDING DOMINATING REALS WITH THE RANDOM ALGEBRA HAIM JUDAH AND SAHARON SHELAH
"... Abstract. We show that there are two models M C N such that by forcing with (Random) ^ over N we add dominating reals. This answers a question of A. Miller. Let R he the random real forcing. It is well known that R is an aAwbounding forcing notion, that is (V / e/n VR3g eco^n V)(Vn e co)(j(n) < ..."
Abstract
 Add to MetaCart
; g(n)). For more detail and notation the reader should see [Ku]. The following is also known [BJ2]: In VRxR there are Cohen reals over V. From this we can conclude the following. There are models M c N such that in NRnM there are unbounded reals over N. (Take N = MR and use the previous result
Results 1  10
of
30