Fundamental Properties of Infinite Trees

Abstrwt. Infinite trees naturally arise in the formaliration and the c~udy of fhc \cm;lntic*, 01 prog-amming languages. This paper investigates some of their i:omninatorial and :iIgcbri\ic propei ties that are especially relevant to semantics. This paper is concerned in particular with regtilar and algchraic itlfinitc trees, rlor ln.ith rzg\lI;lr or algebraic s4f.s of infinite trees. For this reason moss of the propertics s~atcd in rhi$ IVOIX become trivial when restricted either to tinite trees or to infinite words. It present:, a synthesis of various aspects of infinite trees, invcstigatcd bc diIlt*ic*nt ,tuthor\ III differenr contlbxts and hopes to he a unifying step towards a theor! of infinite trct.4 tlliit coultl take place near the theory of formal languages and the combina:,:r::c of tk* free monoi,.,

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