begin{corollary-list}
  item Let x be real number. You can choose a real number y greater than x.
  item Let q be rational number. You can choose a rational number z greater than q.
end{corollary-list}

documentclass{article}
usepackage{amsmath,amsthm,amsfonts,amssymb}
newtheorem{mytheorem}{Theorem}[section]
newenvironment{corollary}
{addtocounter{mytheorem}{1} noindenttextbf{Corollary thesection.arabic{mytheorem}}. begin{itshape}}
{end{itshape}}
newenvironment{corollaries}{begin{itemize} renewcommandlabelitemi{$blacksquare$}}
{end{itemize}}

begin{document}
begin{corollaries}
item begin{corollary} corollary 1 end{corollary}
item begin{corollary} corollary 2 end{corollary}
end{corollaries}

end{document}