diff --git a/availability/classes/info_module.php b/availability/classes/info_module.php
index 952aa7b8474..4091c747a9d 100644
--- a/availability/classes/info_module.php
+++ b/availability/classes/info_module.php
@@ -129,7 +129,7 @@ class info_module extends info {
             return $sectionresult;
         }
 
-        return array('(' . $sectionresult[0] . ') INTERSECT (' . $moduleresult[0] . ')',
+        return array($DB->sql_intersect(array($sectionresult[0], $moduleresult[0]), 'id'),
                 array_merge($sectionresult[1], $moduleresult[1]));
     }
 
diff --git a/availability/classes/tree.php b/availability/classes/tree.php
index 49cfc80c882..218748c1813 100644
--- a/availability/classes/tree.php
+++ b/availability/classes/tree.php
@@ -351,6 +351,7 @@ class tree extends tree_node {
     }
 
     public function get_user_list_sql($not, info $info, $onlyactive) {
+        global $DB;
         // Get logic flags from operator.
         list($innernot, $andoperator) = $this->get_logic_flags($not);
 
@@ -381,17 +382,16 @@ class tree extends tree_node {
 
         // Combine results using INTERSECT or UNION.
         $outsql = null;
-        $outparams = null;
+        $subsql = array();
+        $outparams = array();
         foreach ($childresults as $childresult) {
-            if (!$outsql) {
-                $outsql = '(' . $childresult[0] . ')';
-                $outparams = $childresult[1];
-            } else {
-                $outsql .= $andoperator ? ' INTERSECT (' : ' UNION (';
-                $outsql .= $childresult[0];
-                $outsql .= ')';
-                $outparams = array_merge($outparams, $childresult[1]);
-            }
+            $subsql[] = $childresult[0];
+            $outparams = array_merge($outparams, $childresult[1]);
+        }
+        if ($andoperator) {
+            $outsql = $DB->sql_intersect($subsql, 'id');
+        } else {
+            $outsql = '(' . join(') UNION (', $subsql) . ')';
         }
         return array($outsql, $outparams);
     }
diff --git a/lib/dml/moodle_database.php b/lib/dml/moodle_database.php
index 499e406b75e..ce28102e1b8 100644
--- a/lib/dml/moodle_database.php
+++ b/lib/dml/moodle_database.php
@@ -2226,6 +2226,29 @@ abstract class moodle_database {
         return '';
     }
 
+    /**
+     * Returns the SQL that allows to find intersection of two or more queries
+     *
+     * @since Moodle 2.8
+     *
+     * @param array $selects array of SQL select queries, each of them only returns fields with the names from $fields
+     * @param string $fields comma-separated list of fields (used only by some DB engines)
+     * @return string SQL query that will return only values that are present in each of selects
+     */
+    public function sql_intersect($selects, $fields) {
+        if (!count($selects)) {
+            throw new coding_exception('sql_intersect() requires at least one element in $selects');
+        } else if (count($selects) == 1) {
+            return $selects[0];
+        }
+        static $aliascnt = 0;
+        $rv = '('.$selects[0].')';
+        for ($i = 1; $i < count($selects); $i++) {
+            $rv .= " INTERSECT (".$selects[$i].')';
+        }
+        return $rv;
+    }
+
     /**
      * Does this driver support tool_replace?
      *
diff --git a/lib/dml/mysqli_native_moodle_database.php b/lib/dml/mysqli_native_moodle_database.php
index 11b53bf684a..a27147a63a5 100644
--- a/lib/dml/mysqli_native_moodle_database.php
+++ b/lib/dml/mysqli_native_moodle_database.php
@@ -1601,6 +1601,37 @@ class mysqli_native_moodle_database extends moodle_database {
         return ' CAST(' . $fieldname . ' AS SIGNED) ';
     }
 
+    /**
+     * Returns the SQL that allows to find intersection of two or more queries
+     *
+     * @since Moodle 2.8
+     *
+     * @param array $selects array of SQL select queries, each of them only returns fields with the names from $fields
+     * @param string $fields comma-separated list of fields
+     * @return string SQL query that will return only values that are present in each of selects
+     */
+    public function sql_intersect($selects, $fields) {
+        if (count($selects) <= 1) {
+            return parent::sql_intersect($selects, $fields);
+        }
+        $fields = preg_replace('/\s/', '', $fields);
+        static $aliascnt = 0;
+        $falias = 'intsctal'.($aliascnt++);
+        $rv = "SELECT $falias.".
+            preg_replace('/,/', ','.$falias.'.', $fields).
+            " FROM ($selects[0]) $falias";
+        for ($i = 1; $i < count($selects); $i++) {
+            $alias = 'intsctal'.($aliascnt++);
+            $rv .= " JOIN (".$selects[$i].") $alias ON ".
+                join(' AND ',
+                    array_map(
+                        create_function('$a', 'return "'.$falias.'.$a = '.$alias.'.$a";'),
+                        preg_split('/,/', $fields))
+                );
+        }
+        return $rv;
+    }
+
     /**
      * Does this driver support tool_replace?
      *
diff --git a/lib/dml/tests/dml_test.php b/lib/dml/tests/dml_test.php
index 3d0b6c46be8..8ca100c65f4 100644
--- a/lib/dml/tests/dml_test.php
+++ b/lib/dml/tests/dml_test.php
@@ -5252,6 +5252,88 @@ class core_dml_testcase extends database_driver_testcase {
         $totaldbqueries = $DB->perf_get_reads() + $DB->perf_get_writes();
         $this->assertEquals($totaldbqueries, $DB->perf_get_queries());
     }
+
+    public function test_sql_intersect() {
+        $DB = $this->tdb;
+        $dbman = $this->tdb->get_manager();
+
+        $tables = array();
+        for ($i = 0; $i < 3; $i++) {
+            $table = $this->get_test_table('i'.$i);
+            $table->add_field('id', XMLDB_TYPE_INTEGER, '10', null, XMLDB_NOTNULL, XMLDB_SEQUENCE, null);
+            $table->add_field('ival', XMLDB_TYPE_INTEGER, '10', null, null, null, null);
+            $table->add_field('name', XMLDB_TYPE_CHAR, '255', null, null, null, '0');
+            $table->add_key('primary', XMLDB_KEY_PRIMARY, array('id'));
+            $dbman->create_table($table);
+            $tables[$i] = $table;
+        }
+        $DB->insert_record($tables[0]->getName(), array('ival' => 1, 'name' => 'One'), false);
+        $DB->insert_record($tables[0]->getName(), array('ival' => 2, 'name' => 'Two'), false);
+        $DB->insert_record($tables[0]->getName(), array('ival' => 3, 'name' => 'Three'), false);
+        $DB->insert_record($tables[0]->getName(), array('ival' => 4, 'name' => 'Four'), false);
+
+        $DB->insert_record($tables[1]->getName(), array('ival' => 1, 'name' => 'One'), false);
+        $DB->insert_record($tables[1]->getName(), array('ival' => 2, 'name' => 'Two'), false);
+        $DB->insert_record($tables[1]->getName(), array('ival' => 3, 'name' => 'Three'), false);
+
+        $DB->insert_record($tables[2]->getName(), array('ival' => 1, 'name' => 'One'), false);
+        $DB->insert_record($tables[2]->getName(), array('ival' => 2, 'name' => 'Two'), false);
+        $DB->insert_record($tables[2]->getName(), array('ival' => 5, 'name' => 'Five'), false);
+
+        // Intersection on the int column.
+        $params = array('excludename' => 'Two');
+        $sql1 = 'SELECT ival FROM {'.$tables[0]->getName().'}';
+        $sql2 = 'SELECT ival FROM {'.$tables[1]->getName().'} WHERE name <> :excludename';
+        $sql3 = 'SELECT ival FROM {'.$tables[2]->getName().'}';
+
+        $sql = $DB->sql_intersect(array($sql1), 'ival') . ' ORDER BY ival';
+        $this->assertEquals(array(1, 2, 3, 4), $DB->get_fieldset_sql($sql, $params));
+
+        $sql = $DB->sql_intersect(array($sql1, $sql2), 'ival') . ' ORDER BY ival';
+        $this->assertEquals(array(1, 3), $DB->get_fieldset_sql($sql, $params));
+
+        $sql = $DB->sql_intersect(array($sql1, $sql2, $sql3), 'ival') . ' ORDER BY ival';
+        $this->assertEquals(array(1),
+            $DB->get_fieldset_sql($sql, $params));
+
+        // Intersection on the char column.
+        $params = array('excludeival' => 2);
+        $sql1 = 'SELECT name FROM {'.$tables[0]->getName().'}';
+        $sql2 = 'SELECT name FROM {'.$tables[1]->getName().'} WHERE ival <> :excludeival';
+        $sql3 = 'SELECT name FROM {'.$tables[2]->getName().'}';
+
+        $sql = $DB->sql_intersect(array($sql1), 'name') . ' ORDER BY name';
+        $this->assertEquals(array('Four', 'One', 'Three', 'Two'), $DB->get_fieldset_sql($sql, $params));
+
+        $sql = $DB->sql_intersect(array($sql1, $sql2), 'name') . ' ORDER BY name';
+        $this->assertEquals(array('One', 'Three'), $DB->get_fieldset_sql($sql, $params));
+
+        $sql = $DB->sql_intersect(array($sql1, $sql2, $sql3), 'name') . ' ORDER BY name';
+        $this->assertEquals(array('One'), $DB->get_fieldset_sql($sql, $params));
+
+        // Intersection on the several columns.
+        $params = array('excludename' => 'Two');
+        $sql1 = 'SELECT ival, name FROM {'.$tables[0]->getName().'}';
+        $sql2 = 'SELECT ival, name FROM {'.$tables[1]->getName().'} WHERE name <> :excludename';
+        $sql3 = 'SELECT ival, name FROM {'.$tables[2]->getName().'}';
+
+        $sql = $DB->sql_intersect(array($sql1), 'ival, name') . ' ORDER BY ival';
+        $this->assertEquals(array(1 => 'One', 2 => 'Two', 3 => 'Three', 4 => 'Four'),
+            $DB->get_records_sql_menu($sql, $params));
+
+        $sql = $DB->sql_intersect(array($sql1, $sql2), 'ival, name') . ' ORDER BY ival';
+        $this->assertEquals(array(1 => 'One', 3 => 'Three'),
+            $DB->get_records_sql_menu($sql, $params));
+
+        $sql = $DB->sql_intersect(array($sql1, $sql2, $sql3), 'ival, name') . ' ORDER BY ival';
+        $this->assertEquals(array(1 => 'One'),
+            $DB->get_records_sql_menu($sql, $params));
+
+        // Drop temporary tables.
+        foreach ($tables as $table) {
+            $dbman->drop_table($table);
+        }
+    }
 }
 
 /**