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\begin{document}

% Nastavimo naslov
\title{ČŠŽ čšž}
\author{Miha Novak}
\date{} % Prazen datum

\maketitle % Dejansko naredimo naslov

\begin{abstract}
  To je povzetek enega zelo zanimivega članka.
\end{abstract}

% \   "navaden presledek, ki ni konec stavka"
% ~   "navaden nedeljiv presledek.

V 17.~stoletju še niso imeli elektrike, ki jo je ha izumilil šele kasneje N.~Tesla. Lskj lksj lkj lj lj lj lkjjkjl. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec in dui vehicula, imperdiet arcu a, fringilla sapien. Suspendisse elementum odio eget pretium blandit. Quisque a orci orci. Pellentesque malesuada a nulla quis iaculis. Nunc bibendum fringilla lobortis. Fusce massa mauris, blandit sit amet elementum eget, imperdiet nec nibh. Integer maximus tortor non nisi scelerisque, rhoncus semper leo blandit. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Cras nibh odio, faucibus eget accumsan eget, interdum ut metus. Vivamus finibus purus vitae sem maximus, id consequat quam gravida. Aenean ac libero ex.

Pitagora je dokazal, da velja
%
\begin{equation*}
  a^2 + b^2 = c^2
\end{equation*}
%
za vsa pozitivna realna števila $a$, $b$ in $c$. To so v resnici vedeli že Babilonci, a so
vse delali na glinenih ploščicah.

Gospa Leban-Mrvar je prišla po stopnicah. % vezaj

Obravnavali smo izrek Banach--Tarski. V letih 1992--94 je bilo slabo vreme---čeprav je tudi snežilo---in vsi so bili srečni. Ali pa $a - b$.

Jedla je fižol, kar se ni dobro končalo.

Jedla je {f}{i}{ž}{o}{l}, kar se ni dobro končalo.

VAS

{V}{A}{S}

Naj bo $\powinh{A}$ množica vseh nepraznih podmnožic množice~$A$.

Naj bo $\mathcal{P}_{*}(A)$ množica vseh nepraznih podmnožic množice~$A$.

To je moj makro $\mojmakro{a}{b}{(U+V)}$.


Let us be more precise. A set $A$ is \emph{countable}, or \emph{enumerable}, if there is a
surjection $e : \NN \to \one+ A$, where summing the codomain with the singleton~$\one$
incorporates the empty set $\emptyset$ among the countable ones. When $A$ is inhabited it
suffices to consider surjections $\NN \to A$. The countable subsets of a set~$A$ are the
restrictions of images of maps $\NN \to 1 + A$ to $A$, and they again form a set
$\enum{A}$. If we let $\CE$ abbreviate $\enum{\NN}$ then the Enumeration Axiom states that
there is a surjection
%
\begin{equation*}
  \W{} : \NN \to \CE.
\end{equation*}
%
We are using standard notation for computability theory because it suggests how the
effective topos validates the Enumeration axiom: $\CE$ is just the object of computably
enumerable sets. When we unravel the realizer for surjectivity of $\W{}$ we find out that
it amounts to $\W{}$ being an acceptable numbering in the sense of Ershov's theory of
numbered sets~\cite{ersov80}.

The last axiom is Markov principle:


\noindent
%
In symbolic form Markov principle states
%
\begin{equation*}
  \all{\alpha \in \two^\NN}
  \lnot (\all{n} \alpha_n = 0)
  \lthen
  \some{n} \alpha_n = 1.
\end{equation*}
%
We use the Enumeration axiom only in Theorem~\ref{thm:wcpo-countable} and Markov principle
only in Proposition~\ref{prop:wso}.

Let us be more precise. A set $A$ is \emph{countable}, or \emph{enumerable}, if there is a
surjection $e : \NN \to \one+ A$, where summing the codomain with the singleton~$\one$
incorporates the empty set $\emptyset$ among the countable ones. When $A$ is inhabited it
suffices to consider surjections $\NN \to A$. The countable subsets of a set~$A$ are the
restrictions of images of maps $\NN \to 1 + A$ to $A$, and they again form a set
$\enum{A}$. If we let $\CE$ abbreviate $\enum{\NN}$ then the Enumeration Axiom states that
there is a surjection
%
\begin{equation*}
  \W{} : \NN \to \CE.
\end{equation*}
%
We are using standard notation for computability theory because it suggests how the
effective topos validates the Enumeration axiom: $\CE$ is just the object of computably
enumerable sets. When we unravel the realizer for surjectivity of $\W{}$ we find out that
it amounts to $\W{}$ being an acceptable numbering in the sense of Ershov's theory of
numbered sets~\cite{ersov80}.

The last axiom is Markov principle:


\noindent
%
In symbolic form Markov principle states
%
\begin{equation*}
  \all{\alpha \in \two^\NN}
  \lnot (\all{n} \alpha_n = 0)
  \lthen
  \some{n} \alpha_n = 1.
\end{equation*}
%
We use the Enumeration axiom only in Theorem~\ref{thm:wcpo-countable} and Markov principle
only in Proposition~\ref{prop:wso}.

Let us be more precise. A set $A$ is \emph{countable}, or \emph{enumerable}, if there is a
surjection $e : \NN \to \one+ A$, where summing the codomain with the singleton~$\one$
incorporates the empty set $\emptyset$ among the countable ones. When $A$ is inhabited it
suffices to consider surjections $\NN \to A$. The countable subsets of a set~$A$ are the
restrictions of images of maps $\NN \to 1 + A$ to $A$, and they again form a set
$\enum{A}$. If we let $\CE$ abbreviate $\enum{\NN}$ then the Enumeration Axiom states that
there is a surjection
%
\begin{equation*}
  \W{} : \NN \to \CE.
\end{equation*}
%
We are using standard notation for computability theory because it suggests how the
effective topos validates the Enumeration axiom: $\CE$ is just the object of computably
enumerable sets. When we unravel the realizer for surjectivity of $\W{}$ we find out that
it amounts to $\W{}$ being an acceptable numbering in the sense of Ershov's theory of
numbered sets~\cite{ersov80}.

The last axiom is Markov principle:


\noindent
%
In symbolic form Markov principle states
%
\begin{equation*}
  \all{\alpha \in \two^\NN}
  \lnot (\all{n} \alpha_n = 0)
  \lthen
  \some{n} \alpha_n = 1.
\end{equation*}
%
We use the Enumeration axiom only in Theorem~\ref{thm:wcpo-countable} and Markov principle
only in Proposition~\ref{prop:wso}.

Let us be more precise. A set $A$ is \emph{countable}, or \emph{enumerable}, if there is a
surjection $e : \NN \to \one+ A$, where summing the codomain with the singleton~$\one$
incorporates the empty set $\emptyset$ among the countable ones. When $A$ is inhabited it
suffices to consider surjections $\NN \to A$. The countable subsets of a set~$A$ are the
restrictions of images of maps $\NN \to 1 + A$ to $A$, and they again form a set
$\enum{A}$. If we let $\CE$ abbreviate $\enum{\NN}$ then the Enumeration Axiom states that
there is a surjection
%
\begin{equation*}
  \W{} : \NN \to \CE.
\end{equation*}
%
We are using standard notation for computability theory because it suggests how the
effective topos validates the Enumeration axiom: $\CE$ is just the object of computably
enumerable sets. When we unravel the realizer for surjectivity of $\W{}$ we find out that
it amounts to $\W{}$ being an acceptable numbering in the sense of Ershov's theory of
numbered sets~\cite{ersov80}.

The last axiom is Markov principle:


\noindent
%
In symbolic form Markov principle states
%
\begin{equation*}
  \all{\alpha \in \two^\NN}
  \lnot (\all{n} \alpha_n = 0)
  \lthen
  \some{n} \alpha_n = 1.
\end{equation*}
%
We use the Enumeration axiom only in Theorem~\ref{thm:wcpo-countable} and Markov principle
only in Proposition~\ref{prop:wso}.

Let us be more precise. A set $A$ is \emph{countable}, or \emph{enumerable}, if there is a
surjection $e : \NN \to \one+ A$, where summing the codomain with the singleton~$\one$
incorporates the empty set $\emptyset$ among the countable ones. When $A$ is inhabited it
suffices to consider surjections $\NN \to A$. The countable subsets of a set~$A$ are the
restrictions of images of maps $\NN \to 1 + A$ to $A$, and they again form a set
$\enum{A}$. If we let $\CE$ abbreviate $\enum{\NN}$ then the Enumeration Axiom states that
there is a surjection
%
\begin{equation*}
  \W{} : \NN \to \CE.
\end{equation*}
%
We are using standard notation for computability theory because it suggests how the
effective topos validates the Enumeration axiom: $\CE$ is just the object of computably
enumerable sets. When we unravel the realizer for surjectivity of $\W{}$ we find out that
it amounts to $\W{}$ being an acceptable numbering in the sense of Ershov's theory of
numbered sets~\cite{ersov80}.

The last axiom is Markov principle:


\noindent
%
In symbolic form Markov principle states
%
\begin{equation*}
  \all{\alpha \in \two^\NN}
  \lnot (\all{n} \alpha_n = 0)
  \lthen
  \some{n} \alpha_n = 1.
\end{equation*}
%
We use the Enumeration axiom only in Theorem~\ref{thm:wcpo-countable} and Markov principle
only in Proposition~\ref{prop:wso}.

Let us be more precise. A set $A$ is \emph{countable}, or \emph{enumerable}, if there is a
surjection $e : \NN \to \one+ A$, where summing the codomain with the singleton~$\one$
incorporates the empty set $\emptyset$ among the countable ones. When $A$ is inhabited it
suffices to consider surjections $\NN \to A$. The countable subsets of a set~$A$ are the
restrictions of images of maps $\NN \to 1 + A$ to $A$, and they again form a set
$\enum{A}$. If we let $\CE$ abbreviate $\enum{\NN}$ then the Enumeration Axiom states that
there is a surjection
%
\begin{equation*}
  \W{} : \NN \to \CE.
\end{equation*}
%
We are using standard notation for computability theory because it suggests how the
effective topos validates the Enumeration axiom: $\CE$ is just the object of computably
enumerable sets. When we unravel the realizer for surjectivity of $\W{}$ we find out that
it amounts to $\W{}$ being an acceptable numbering in the sense of Ershov's theory of
numbered sets~\cite{ersov80}.

The last axiom is Markov principle:


\noindent
%
In symbolic form Markov principle states
%
\begin{equation*}
  \all{\alpha \in \two^\NN}
  \lnot (\all{n} \alpha_n = 0)
  \lthen
  \some{n} \alpha_n = 1.
\end{equation*}
%
We use the Enumeration axiom only in Theorem~\ref{thm:wcpo-countable} and Markov principle
only in Proposition~\ref{prop:wso}.



\end{document}
