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In the random graph G(n,p),p=n^{-a} : if psi has probability 0(n^{-epsilon}) for every epsilon > 0 then it has probability 0(e^{-n^epsilon}) for some epsilon > 0
Saharon Shelah
Shelah Spencer [ShSp:304] proved the 0-1 law for the random graphs G(n,p_n), p_n=n^{- alpha}, alpha in (0,1) irrational (set of nodes in [n]= {1, ...,n}, the edges are drawn indepe…
Set theory without choice: not everything on cofinality is possible
Saharon Shelah
We prove (ZF+DC) e.g. : if mu =|H(mu)| then mu^+ is regular non measurable. This is in contrast with the results for mu = aleph_{omega} on measurability see Apter Magidor [ApMg]
Menas' result is best possible
Arthur Apter, Saharon Shelah
Generalizing some earlier techniques due to the second author, we show that Menas' theorem which states that the least cardinal kappa which is a measurable limit of supercompact or…
A ZFC Dowker space in : an application of pcf theory to topology
Menachem Kojman, Saharon Shelah
A ZFC Dowker space is constructed which has cardinality . This provides a bound in ZFC to the first cardinal in which there is a ZFC Dowker space. The space we constr…
Possibly every real function is continuous on a non--meagre set
Saharon Shelah
We prove consistency of the following sentence: ``ZFC + every real function is continuous on a non-meagre set'', answering a question of Fremlin.
On squares, outside guessing of clubs and I_{<f}[lambda]
Mirna Džamonja, Saharon Shelah
Suppose that lambda = mu^+. We consider two aspects of the square property on subsets of lambda. First, we have results which show e.g. that for aleph_0 <= kappa =cf (kappa)< mu, t…