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In this paper paraconsistent first-order logic LP^{#}_{\omega} withrestricted modus ponens rule and infinite hierarchy levels of contradiction isproposed. Corresponding paraconsistent set theory KSth^{#}_{\omega} isdiscussed.Axiomatical system HST^{#}_{\omega} as paraconsistent generalizationof Hrbacek set theory HST is considered.

Paraconsistent First-Order Logic with restricted modus ponens rule and  infinite hierarchy levels of contradiction $LP^\#_{\omega}$. Axiomatical  system $HST^\#_{\omega}$, as paraconsistent generalization of Hrbacek set  theory HST