@article {IOPORT.04200194, author = {Prati, Nando}, title = {The theory FAST and the induction axiom in finite form.}, year = {1990}, journal = {Rivista di Matematica della Universit\`a di Parma. Serie IV}, volume = {16}, issn = {0035-6298}, pages = {213-222}, publisher = {Universit\`a di Parma, Parma}, abstract = {The Fuzzy Alternative Set Theory (FAST) considers objects satisfying aspects both of Fuzzy Set Theory and of Alternative Set Theory (AST). FAST has been introduced in the author's earlier paper [ibid. 14, 181-191 (1988; Zbl 0688.03035)]. As in AST, in FAST it is interesting to substitute the full axiom of induction with the axiom saying that induction is satisfied only for the formulas that can be written down finitely: this version of the axiom cannot be written down formally. In the paper it is shown that there is an axiom that can be written down formally and is equivalent to the axiom of induction for finite formulas.}, reviewer = {N.Prati}, identifier = {04200194}, }