Clones and Genoids in Lambda Calculus and First Order Logic Zhaohua Luo Abstract: A genoid is a system (A, G, x, +) consists of a monoid (G, e), a right act A of G, x in A, + in G, such that for any a in A and u in G there is a unique element [a, u] in G such that x[a, u] = a and +[a, u] = u. A genoid represents a category with two objects such that one is the product of itself with the other. For any right act P of G, we define a new right act P^A = (P, *) by a*u = a[x, u], which is the exponent in the cartesian closed category of right acts of G. We define a lambda calculus to be a genoid (A, G) together with homomorphisms L: A^A -> A and A X A -> A such that (La)+x = a and L(a+x) = a for any a in A. This means that A^A and A are isomorphic as right acts of G. A quantifier algebra for a genoid (A, G) is a right act P of G, together with homomorphisms E: P^A -> P, F: P^0 -> P, and =>: P X P -> P, such that p for any p, q in P: (i) {F, =>} defines a Boolean algebra P. (ii) E (p V q) = (E p) V (E q). (iii) p < E p. http://www.algebraic.net/cag/cag.pdf Clones and Genoids Homepage: http://www.algebraic.net/cag/