Concerning R. L. Moore's axiom $5$

CONCERNING INTERSECTING CONTINUA BY R. L. MooRu

The Axiom of Determinancy Implies Dependent Choices in L(R)

We prove the following Main Theorem: ZF + AD + V L(R) =>DC. As a corollary we have that Con(ZF + AD) Con(ZF + AD + DC). Combined with the result of Woodin that Con(ZF + AD) Con(ZF + AD + AC') it follows that DC (as well as AC') is independent relative to ZF + AD. It is finally shown (jointly with H. Woodin) that ZF + AD + DCR, where DCR is DC restricted to reals, implies the consistency of ZF +...

A Conservation Result concerning Bounded Theofues and the Collection Axiom

We present two proofs, one proof-theoretic and one model-theoretic, showing that 0 adding the BE1-collection axioms to any bounded first-order theory R of arithmetic 0 yields an extension which is VC1-conservative over R. Preliminaries. A theory of arithmetic R contains the non-logic symbols 0, S, +, = , and 6 . R may contain further non-logical symbols; in particular, S2 is a theory of arithme...

A Conservation Result concerning Bounded Theories and the Collection Axiom

We present two proofs, one proof-theoretic and one model-theoretic, showing that adding the ß ^-collection axioms to any bounded first-order theory R of arithmetic yields an extension which is V ̂ -conservative over R. Preliminaries. A theory of arithmetic R contains the nonlogic symbols 0, S, +, ■, and < . R may contain further nonlogical symbols; in particular S2 is a theory of arithmetic [1]....

THE URYSOHN AXIOM AND THE COMPLETELY HAUSDORFF AXIOM IN L-TOPOLOGICAL SPACES

In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to L-topological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived