Append i x F Free Lattices Ralph

About Free Lattices and Free Modular Lattices

Ralph Freese Department of Mathematics University of Hawaii at Manoa Honolulu, Hawaii 96822 In this paper we look at some of the problems on free lattices and free modular lattices which are of an order theoretic nature. We review some of the known results, give same new results, and present several open problems. Every countable partially ordered set can be order embedded into a countable free...

Planar sublattices of FM ( 4 )

R. McKenzie, A. Kostinsky and B. J6nsson have proved the remarkable result that the class of finite sublattices of a free lattice and the class of finite projective lattices coincide [6]. I f we restrict ourselves to modular lattices, the above result is no longer true. Examining the map from the free modular lattice on three generators, FM(3), to the free distributive lattice on three generato...

Algebras, Lattices, Varieties Volume I

Ordinal Sums of Projective Lattices and Isotone Sections

A lattice L is projective in a variety V of lattices if whenever f : K L is an epimorphism, there is a homomorphism g : L→ K such that f(g(a)) = a for all a ∈ L. Note g is one-to-one and ρ = gf : K→ K is a retraction of K; that is, ρ is an endomorphism of K and ρ2 = ρ. The sublattice ρ(K) = g(L) of K is isomorphic to L. The image g(L) is a retract of K. In a slight abuse of terminology, we will...

leanCoP: lean connection-based theorem proving

The Prolog program "prove(M,I) :append(Q,[C|R],M), \+member(-_,C), append(Q,R,S), prove([!],[[-!|C]|S],[],I). prove([],_,_,_). prove([L|C],M,P,I) :(-N=L; -L=N) -> (member(N,P); append(Q,[D|R],M), copy_term(D,E), append(A,[N|B],E), append(A,B,F), (D==E -> append(R,Q,S); length(P,K), K<I, append(R,[D|Q],S)), prove(F,S,[L|P],I)), prove(C,M,P,I)." implements a theorem prover for classical first-ord...