Table of contents : Constructible semi-lattices of degrees of constructibility....Pages 1-43 Refining systems on Boolean algebras....Pages 45-58 The Lindenbaum-algebra of the theory of well-orders and Abelian groups with the quantifier Q α ....Pages 59-73 Extendability of structures as infinitary property....Pages 75-93 A reduction of the theory of types....Pages 95-100 Random forcing....Pages 101-117 Topological problems in alternative set theory....Pages 119-133 On the Baire property of Boolean algebras....Pages 135-141 The relation between ε — δ procedures and the infinitely small in nonstandard methods....Pages 143-152 Structures Σ — saturee....Pages 153-168 On the inhomogenity of the set of P(m)-points of ω*....Pages 169-179 On the projective class of the continuum hypothesis....Pages 181-185 A survey of finite-type Recursion....Pages 187-209 Initial segments of models of Peano's axioms....Pages 211-226 On the rules of proof generated by hierarchies....Pages 227-239 On cardinal numbers in Quine's New Foundations....Pages 241-250 The theory of the class HOD....Pages 251-255 Construction of nice trees....Pages 257-271 Differential calculus in the alternative set theory....Pages 273-284 The consistency of the theory ZF+L 1 ≠HOD....Pages 285-290 On the decidability of the theory of linear orderings in the language L(Q 1 )....Pages 291-304 On the theories of end-extensions of models of arithmetic....Pages 305-310 Some properties of filters....Pages 311-328 More constructively about the constructibility....Pages 329-358