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
  In this paper paraconsistent first-order logic LP^{#}_{\omega} with restricted modus ponens rule and infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#}_{\omega} is discussed.Axiomatical system HST^{#}_{\omega} as paraconsistent generalization of Hrbacek set theory HST is considered. 
Jaykov Foukzon