Note on inductive finiteness in mereology.

A Note on Kneser-haken Finiteness

Kneser-Haken Finiteness asserts that for each compact 3-manifold M there is an integer c(M) such that any collection of k > c(M) closed, essential, 2-sided surfaces in M must contain parallel elements. We show here that if M is closed then twice the number of tetrahedra in a (pseudo)triangulation of M suffices for c(M).

A Note on Inductive Generalization

A Note on Finiteness in the Predicative Foundations of Arithmetic

In a sequence of two papers, Solomon Feferman and Geoffrey Hellman ([FH95], [FH98]) introduced formal contexts in which they established the existence and categoricity of a natural number structure by predicative means given the primitive notion of a finite set of individuals and given also that these individuals have some structure as built up by ordered pairs (Peter Aczel had a crucial contri...

A Further Note on Inductive Generalization

In this paper, we develop the algorithm, given in Plotkin (1970), for finding the least generalization of two clauses, into a theory of inductive generalization. The types of hypothesis which can be formed are very simple. They all have the form: (x)Pxm Qx. We have been guided by ideas from the philosophy of science, following Buchanan (1966). There is no search for infallible methods of genera...

A Note on Binary Inductive Logic

We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfy...